Blocking Artifacts Caused by Image Compression
Many image compression methods are based on block transform coding. These include still image compression procedures, such as JPEG, and video compression procedures, such as MPEG and H.264/AVC.
Block transform coding can cause blocking artifacts due to quantization errors at boundaries of blocks. Blocking effects are considered the most annoying artifacts of compressed images, and can dramatically degrade a visual quality especially when the images are encoded at high compression rates. The compression techniques in most coding standards cause high frequency quantization errors in individual blocks of pixels, resulting in discontinuities at block boundaries. To achieve high quality image compression using block based transform codes, the reduction of blocking artifacts in decompressed output images is critical.
Several methods post-process compressed images to improve the visual quality. Some methods analyze a spatial domain in the image, while others analyze a frequency domain. There also are iterative methods based on projections onto convex sets. In addition, processing images can adaptively reduce artifacts, while preserving edges. A large number of methods that reduce blocking artifacts include: projections onto convex sets (POCS), spatial block boundary filtering, wavelet filtering methods, statistical modeling methods, and constrained optimization methods.
Some of the more effective deblocking techniques are based on shifted transforms. That technique was first used with the re-application of shifted JPEG coded images.
Shifted transform procedures can improve the visual quality over conventional techniques based on POCS, and wavelet transforms. In the simplified version of the shifted JPEG transform, the transform operator is a discrete cosine transform (DCT) in the spatial and frequency domains. A filter operator is a combined quantization and dequantization process based on a quantization matrix. An averaging process is an unweighted average of the inverse shifted images. An improved weighted averaging scheme can adapt to the input image content.
Those methods tend to be computational complex, and have an explicit dependency on correct image gradient information. Those methods are also sensitive to preset parameters.
Dictionary Learning
Dictionary learning constructs an over-complete bases and represents image patches sparsely using these bases. Sparsity is a term of art in signal and data processing, where any zero coefficients in signals or data are substantially larger than the number of non-zero-coefficients.
Dictionary learning constructs a dictionary D and a reconstruction coefficient matrix A(i, j) by minimizing
                                                    X            -            DA                                    F        2            +              λ        ⁢                                          A                                1                      ,                  ⁢    where                                          A                          1            :=                        ∑                      i            ,            j                          ⁢                                        A            ⁡                          (                              i                ,                j                            )                                                      ,  λ is a Lagrangian multiplier to determine the weighted sum of fidelity and sparsity terms. Columns of X represent patches of an image, and F is the Frobenius norm. Each column is a vectorized patch. Dictionary learning provides solutions for compression, denoising and other inverse problems in image processing. Some methods use group structures for dictionary learning.